It is understood Depp disembarked from his private jet at Brisbane's old international terminal, which was used to greet delegates during last year's G20 leaders' summit.

Pistol and Boo, with dog groomers Lianne and Ellie Kent, who unwittingly alerted authorities to their presence in the country.

Photo: Happy Dogz

Both the Brisbane Airport Corporation and Hawkers Aviation, which handles VIP arrivals and departures at the airport, referred queries to Australian Customs.

Minister takes tough line

Dog threat: Barnaby Joyce.

Photo: Andrew Meares

Mr Joyce did not mince words in expressing his displeasure in Depp bypassing strict quarantine laws, accusing him of sneaking them into the country.

"We found out he snuck them in because we saw him taking them to a poodle groomer," he said.

Johnny Depp with one of his Yorkshire Terriers.

Photo: Pinterest

"Now Mr Depp has to either take his dogs back to California or we're going to have to euthanise them."

Groomer sad for Depp and dogs

Dog groomer Lianne Kent, from the Happy Dogz salon in Gold Coast's north, says Depp and his wife, model and actor Amber Heard, must be having a hard time dealing with the situation.

"I'm upset about it. I feel sorry for them," Ms Kent said on Thursday.

"I can't imagine what they'll be going through."

Ms Kent said the dogs - Pistol and Boo - looked immaculate when she groomed them on Saturday.

"Dogs usually come in messy when I groom them, but they looked beautiful," she said.

"They smelled amazing.

"I did a full groom, bath and trimming. They were just gorgeous dogs - they'd just sit there."

However, Ms Kent may have inadvertently tipped off officials to the dogs' Australian adventure by sharing photos of them at her salon with the media.

Public support for Pistol and Boo

Mr Joyce's euthanasia threats do not appear to have won much public support.

A change.org petition directed at Mr Joyce titled, "Save Johnny Depp's dogs from being euthenized [sic] by the Australian Government!" gathered more than 1500 signatures in just three hours on Thursday morning.

A parody Twitter account has also been established in the dog's names.

Stars aren't above the law: minister

Mr Joyce quipped that he was unlikely to be invited to the premiere of the latest instalment in the highly successful Pirates of the Caribbean franchise but said Depp's star status did not exempt him from obeying quarantine laws.

"Just because he's Johnny Depp does not mean he's exempt from Australian law," he told 612 ABC Brisbane.

"There is a process if you want to bring animals in, you get the permits, they go into quarantine and then you can have them.

"You start letting in movie stars, even though they have been the sexiest man alive twice, who come into our nation, why don't we just break the laws for everybody.

"If dogs come in and they have rabies ... the whole life in Brisbane changes. They won't be so sympathetic to Depp at that point in time," he said.

"Think how close it is, it's in Bali, just next door, it's not fanciful stuff. Therefore, we are very diligent about what comes into our nation."

Mr Joyce said Boo and Pistol's presence in the country was discovered when they were taken to Gold Coast dog groomers Happy Dogz and accused Depp of sneaking them in to the country.

'We rely on people being honest'

"He has decided to bring in to our nation two dogs without actually getting the proper certification and proper permits required. It basically looks like he snuck them in," he said.

"In my view, he's a great actor, Jack Sparrow, wonderful, but this is not an excuse for breaking our laws.

"We rely on people being honest ... most reasonable people say, 'I do have a couple of dogs, I'd better put that on the piece of paper.' "

"If he really can't live without Pistol and Boo, if life is impossible without Pistol and Boo, he has to get them to go through the appropriate quarantine process where they would hold them in quarantine facilities like all the other dogs."

Minister rules out offering 10-day quarantine

The minimum quarantine period for animals entering Australia is 10 days but Mr Joyce said he would not offer the option of Depp's dogs now going into quarantine.

"I'm dead against that idea and this idea that I break the law and then we go in another direction just because I'm a movie star; I don't like that," he said.

"If you want to obey the law, you have 10 days to quarantine."

Media camped out

A large media contingent has set up camp outside superbike star Mick Doohan's sprawling Gold Coast estate, all desperate for a glimpse of Depp's suddenly famous dogs, Boo and Pistol.

Eleven cars, even more journalists and the odd helicopter are staking out the 18-hectare Coomera property in the hope the Pirates of the Caribbean star ventures out to hand his pooches in to customs officials.

A Channel Nine crew in a chopper reportedly spotted the Yorkshire terriers through a window but otherwise, there's been no sign of the most talked about pets since Paris Hilton's chihuahua, Tinkerbell.

Those in the handful of cars to drive past the boab trees and through Doohan's big white gate haven't given anything away but one found the situation amusing enough to pull out his phone to shoot some video of his own as the cameras rolled.